A riemannian-geometry approach for dynamics and control of object manipulation under constraints

Suguru Arimoto, Morio Yoshida, Masahiro Sekimoto, Kenji Tahara

研究成果: 書籍/レポート タイプへの寄稿会議への寄与

5 被引用数 (Scopus)

抄録

A Riemannian-geometry approach for control and stabilization of dynamics of object manipulation under holonomic or non-holonomic (but Pfaffian) constraints is presented. First, position/force hybrid control of an endeffector of a multijoint redundant (or nonredundant) robot under a nonholonomic constraint is reinterpreted in terms of "submersion" in Riemannian geometry. A force control signal constructed in the image space spanned from the constraint gradient can be regarded as a lifting in the direction orthogonal to the kernel space. By means of the Riemannian distance on the constraint submanifold, stability on a manifold for a redundant system under holonomic constraints is discussed. Second, control and stabilization of dynamics of two-dimensional object grasping and manipulation by using a pair of multi-joint robot fingers are tackled, when a rigid object is given with arbitrary shape. Then, it is shown that rolling contact constraint induce the Euler equation of motion in an implicit function form, in which constraint forces appear as wrench vectors affecting on the object. The Riemannian metric can be introduced in a natural way on a constraint submanifold induced by rolling contacts. A control signal called "blind grasping" is defined and shown to be effective in stabilization of grasping without using the details of information of object shape and parameters or external sensing. The concept of stability of the closedloop system under constraints is renewed in order to overcome the degrees-of-freedom redundancy problem. An extension of Dirichlet-Lagrange's stability theorem to a system of DOFredundancy under constraints is presented by using a Morse- Lyapunov function.

本文言語英語
ホスト出版物のタイトル2009 IEEE International Conference on Robotics and Automation, ICRA '09
ページ1683-1690
ページ数8
DOI
出版ステータス出版済み - 11月 2 2009
イベント2009 IEEE International Conference on Robotics and Automation, ICRA '09 - Kobe, 日本
継続期間: 5月 12 20095月 17 2009

出版物シリーズ

名前Proceedings - IEEE International Conference on Robotics and Automation
ISSN(印刷版)1050-4729

その他

その他2009 IEEE International Conference on Robotics and Automation, ICRA '09
国/地域日本
CityKobe
Period5/12/095/17/09

!!!All Science Journal Classification (ASJC) codes

  • ソフトウェア
  • 制御およびシステム工学
  • 人工知能
  • 電子工学および電気工学

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